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The relevance of chaos for the linear response theory

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  • Falcioni, M.
  • Vulpiani, A.

Abstract

We discuss the van Kampen objection, about the range of validity of the linear response theory; we show that, in chaotic systems, the instability of the dynamics has a constructive role. For any system with good chaotic properties, a fluctuation response relation holds at macroscopic times, because the relevant perturbative parameter is tc·⋎f⋎, where tc is a correlation time and ⋎f⋎ the strength of the external force. Nevertheless, the van Kampen criticism has relevant consequences on the feasibility of numerical experiments.

Suggested Citation

  • Falcioni, M. & Vulpiani, A., 1995. "The relevance of chaos for the linear response theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 215(4), pages 481-494.
    • Handle: RePEc:eee:phsmap:v:215:y:1995:i:4:p:481-494
    DOI: 10.1016/0378-4371(94)00277-Z
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    1. Kerkvliet, Benedict J., 1978. "Popular Uprisings in the Philippines, 1840–1940. By David R. Sturtevant. (Ithaca, N.Y.: Cornell University Press, 1976. Pp. 317. $17.50.)," American Political Science Review, Cambridge University Press, vol. 72(2), pages 771-772, June.
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